For a LTE base station is it possible to determine the relationship
between the signal strength and distance?
Ideally yes. Practically, probably not very reliably. Given the following pieces of information and assumptions, you can find the distance between any transmitter and receiver:
The transmitting antenna's radiation pattern and orientation (gain)
SC-FDMA is encoded and transmitted from the handset where there are power tradeoffs. This encoding is better than OFDMA for the handset for the following related reasons:
Reduces peak to average power ratio
Increases efficiency of the power amplifier
Increases battery life
So at the base station they can employ transmitters that can handle a higher peak ...
You can see this information if you enter "field test mode". Google that for device specific instructions. It should show you the name or serial number of the base station you are connected to, but I'm not sure if you can use that to find it's physical location, although I haven't tried.
On iPhones the signal strength indicator can be changed to a numerical value as indicated by the image below.
The above can be done by dialing *3001#12345#*. The phone will enter into field test mode. The value indicated is in dBm. Lower dbm value indicates a poor signal. A dBm value closer to 0 is a strong signal.
Similarly on a Android phone the same ...